Two cards are drawn at random from an ordinary deck of 52 cards. Determine the probability that both cards are aces if

Question

a) The first card is replaced before the second card is drawn.

b) the first card is not replaced before the second card is drawn

Answer 1

a) (4/52)(4/52)=(1/13)(1/13)=1/169 (there are 4 aces and the first card is put back)

b) (4/52)(3/51)=(1/13)(1/17)=1/221

another way to look at part b...

there are (52) ways to draw 2 cards from a deck of 52 cards...

                   2

(52!)/(2!)(52-2)!=(52!)/(2!)(50!)=1326 ways

there are (4) ways to draw 2 aces from 4 aces

                  2

(4!)/(2!)(4-2!)=(4!)(2!)(2!)=(4*3*2*1)/(2*1)(2*1)=(4*3)/(2*1)=12/2=6

Probability=6/1326=1/221